Cellular Automata (CA) are a class of computers with a very regular structure such as a Cartesian lattice of cells. In 2 dimensions a CA can be like a checkerboard where the state of each cell or square is represented by whether or not there is a checker on that cell. There are very simple CAs that have the property of being Universal (UCAs). This means that a large enough such UCA could, after being started off in the right state, exactly mimic the behavior of any computer. Another important property of some CAs is that they are reversible. One set of rules can run the CA forwards, and another set can run it backwards so that it exactly retraces its steps in the reverse order. Finally, there are simple Reversible, Universal Cellular Automata (RUCAs) and they are the bases of the discrete models of physics that are used in Digital Mechanics. Every time step, a simple rule causes the states of various cells to change, depending on the states of other nearby cells.
If space-time is discrete, then we believe that one of the simpler representations of state, which includes charge, motion and angular momentum, is by means of a Reversible Universal Cellular Automaton (RUCA [1] ) that is a Discrete Second Order System (DSOS). A second order system represents dynamic information by representing the positional state at 2 neighboring points in time. A DSOS RUCA can do everything demanded by physics with regard to reversibility with CPT symmetry, and do so efficiently that we feel compelled to look more closely at such systems.
The particular system we will describe may appear quite foreign however it has the amazing property that given its design, many properties of physics are represented by configurations of bits. Once the general ideas are understood, we will be able to show how charge, angular momentum, linear momentum and energy can be represented within the model. We will also be able to argue why DP predicts angular isotropy above the scale of quantization and predicts why the laws of physics are independent of the choice of unaccelerated reference frame (at scales greater than the lattice spacing).
The lattice of a DM RUCA is not the space-time of physics. It is the engine of an informational process. In essence, the RUCA runs a computation. As a consequence of that process and of appropriate initial conditions various stable structures will exist in the lattice. For each such stable structure, we expect that its behavior will mimic the behavior of some fundamental particle, such as a Muon or a photon. What we demand of a correct model is that the behavior of those particles obeys the laws of physics and that we can match up the particles of the RUCA with the particles of physics. When DM is mature, measurements made of the behavior of the particles in the RUCA must be consistent with all of our experimental observations of physics such as what is described by quantum mechanics. Further, it should be possible to derive special and general relativity from the basic rules the DM system.
The reader must keep in mind that the lattice of a DM system is a not part of physics, its space is not the space of physics and it does not have to obey the laws of physics. One might think that a Cartesian Lattice has no place in a relativistically correct model of physics. Such thoughts are due to a simple misunderstanding. The statement that a Cartesian RUCA cannot produce relativistically correct physics is equivalent to stating that a particular brand of super-computer is unsuitable for 3-D models of relativistic physics because the geometry of the bits in its memory chips are basically a 2 dimensional Cartesian lattice [2] . Of course, it is not an accident that the local geometry of the RUCA is very similar to the local geometry of space. But the definition of a geodesic is not some straight line across the RUCA lattice, it is the path taken by a photon working its way across the RUCA lattice while reacting properly to gravitational fields that influence its path.
(Last revised 15-Oct-01)
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